dggqrf man page on YellowDog

Man page or keyword search:  
man Server   18644 pages
apropos Keyword Search (all sections)
Output format
YellowDog logo
[printable version]

DGGQRF(l)			       )			     DGGQRF(l)

NAME
       DGGQRF  -  compute a generalized QR factorization of an N-by-M matrix A
       and an N-by-P matrix B

SYNOPSIS
       SUBROUTINE DGGQRF( N, M, P, A, LDA, TAUA, B, LDB,  TAUB,	 WORK,	LWORK,
			  INFO )

	   INTEGER	  INFO, LDA, LDB, LWORK, M, N, P

	   DOUBLE	  PRECISION A( LDA, * ), B( LDB, * ), TAUA( * ), TAUB(
			  * ), WORK( * )

PURPOSE
       DGGQRF computes a generalized QR factorization of an  N-by-M  matrix  A
       and an N-by-P matrix B:
		   A = Q*R,	   B = Q*T*Z,

       where  Q	 is  an	 N-by-N	 orthogonal  matrix,  Z is a P-by-P orthogonal
       matrix, and R and T assume one of the forms:

       if N >= M,  R = ( R11 ) M  ,   or if N < M,  R = ( R11  R12 ) N,
		       (  0  ) N-M			   N   M-N
			  M

       where R11 is upper triangular, and

       if N <= P,  T = ( 0  T12 ) N,   or if N > P,  T = ( T11 ) N-P,
			P-N  N				 ( T21 ) P
							    P

       where T12 or T21 is upper triangular.

       In particular, if B is square and nonsingular, the GQR factorization of
       A and B implicitly gives the QR factorization of inv(B)*A:

		    inv(B)*A = Z'*(inv(T)*R)

       where  inv(B)  denotes  the inverse of the matrix B, and Z' denotes the
       transpose of the matrix Z.

ARGUMENTS
       N       (input) INTEGER
	       The number of rows of the matrices A and B. N >= 0.

       M       (input) INTEGER
	       The number of columns of the matrix A.  M >= 0.

       P       (input) INTEGER
	       The number of columns of the matrix B.  P >= 0.

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,M)
	       On entry, the N-by-M matrix A.  On exit, the  elements  on  and
	       above the diagonal of the array contain the min(N,M)-by-M upper
	       trapezoidal matrix R (R is upper triangular if  N  >=  M);  the
	       elements below the diagonal, with the array TAUA, represent the
	       orthogonal matrix Q as a product of min(N,M) elementary reflec‐
	       tors (see Further Details).

       LDA     (input) INTEGER
	       The leading dimension of the array A. LDA >= max(1,N).

       TAUA    (output) DOUBLE PRECISION array, dimension (min(N,M))
	       The scalar factors of the elementary reflectors which represent
	       the   orthogonal	  matrix   Q   (see   Further	Details).    B
	       (input/output)  DOUBLE  PRECISION  array,  dimension (LDB,P) On
	       entry, the N-by-P matrix B.  On exit, if N <= P, the upper tri‐
	       angle  of the subarray B(1:N,P-N+1:P) contains the N-by-N upper
	       triangular matrix T; if N > P, the elements on  and  above  the
	       (N-P)-th	 subdiagonal  contain  the  N-by-P  upper  trapezoidal
	       matrix T; the remaining elements, with the array	 TAUB,	repre‐
	       sent the orthogonal matrix Z as a product of elementary reflec‐
	       tors (see Further Details).

       LDB     (input) INTEGER
	       The leading dimension of the array B. LDB >= max(1,N).

       TAUB    (output) DOUBLE PRECISION array, dimension (min(N,P))
	       The scalar factors of the elementary reflectors which represent
	       the   orthogonal	  matrix   Z   (see  Further  Details).	  WORK
	       (workspace/output) DOUBLE PRECISION array, dimension (LWORK) On
	       exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The  dimension  of  the array WORK. LWORK >= max(1,N,M,P).  For
	       optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3), where
	       NB1  is the optimal blocksize for the QR factorization of an N-
	       by-M matrix, NB2 is the optimal blocksize for the RQ factoriza‐
	       tion  of an N-by-P matrix, and NB3 is the optimal blocksize for
	       a call of DORMQR.

	       If LWORK = -1, then a workspace query is assumed;  the  routine
	       only  calculates	 the  optimal  size of the WORK array, returns
	       this value as the first entry of the WORK array, and  no	 error
	       message related to LWORK is issued by XERBLA.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value.

FURTHER DETAILS
       The matrix Q is represented as a product of elementary reflectors

	  Q = H(1) H(2) . . . H(k), where k = min(n,m).

       Each H(i) has the form

	  H(i) = I - taua * v * v'

       where taua is a real scalar, and v is a real vector with
       v(1:i-1)	 =  0  and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
       and taua in TAUA(i).
       To form Q explicitly, use LAPACK subroutine DORGQR.
       To use Q to update another matrix, use LAPACK subroutine DORMQR.

       The matrix Z is represented as a product of elementary reflectors

	  Z = H(1) H(2) . . . H(k), where k = min(n,p).

       Each H(i) has the form

	  H(i) = I - taub * v * v'

       where taub is a real scalar, and v is a real vector with
       v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored  on  exit  in
       B(n-k+i,1:p-k+i-1), and taub in TAUB(i).
       To form Z explicitly, use LAPACK subroutine DORGRQ.
       To use Z to update another matrix, use LAPACK subroutine DORMRQ.

LAPACK version 3.0		 15 June 2000			     DGGQRF(l)
[top]

List of man pages available for YellowDog

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net